Statistical Inference of Inverted Exponentiated Rayleigh Distribution under Joint Progressively Type-II Censoring

Fan, Jingwen; Gui, Wenhao

doi:10.3390/e24020171

Cited by 14 publications

(5 citation statements)

References 29 publications

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“…This application offers the analysis of chemistry data, representing the coating weights of iron sheets, collected during January-March 2018 by the Aluminium Africa Limited (ALAF) (commercially) industry in Tanzania. Here, from the ALAF industry, we shall provide a dataset consisting of 72 observations on the coating weight (in gm/m 2 ); see Table 7. Originally, this dataset was first presented by Rao and Mbwambo [36] and reanalyzed later by Fan and Gui [37]. Before proceeding, from Table 7, the estimation results of μ, γ, and KS (p-value) were 0.1441 (0.0132), 283.…”

Section: Coating Weights Of Iron Sheetsmentioning

confidence: 99%

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Elshahhat

Mohammed

2023

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A new two-parameter extended exponential lifetime distribution with an increasing failure rate called the Poisson–exponential (PE) model was explored. In the reliability experiments, an adaptive progressively Type-II hybrid censoring strategy is presented to improve the statistical analysis efficiency and reduce the entire test duration on a life-testing experiment. To benefit from this mechanism, this paper sought to infer the unknown parameters, as well as the reliability and failure rate function of the PE distribution using both the likelihood and product of spacings estimation procedures as a conventional view. For each unknown parameter, from both classical approaches, an approximate confidence interval based on Fisher’s information was also created. Additionally, in the Bayesian paradigm, the given classical approaches were extended to Bayes’ continuous theorem to develop the Bayes (or credible interval) estimates of the same unknown quantities. Employing the squared error loss, the Bayesian inference was developed based on independent gamma assumptions. Because of the complex nature of the posterior density, the Markov chain with the Monte Carlo methodology was used to obtain data from the whole conditional distributions and, therefore, evaluate the acquired Bayes point/interval estimates. Via extensive numerical comparisons, the performance of the estimates provided was evaluated with respect to various criteria. Among different competing progressive mechanisms, using four optimality criteria, the best censoring was suggested. Two real chemical engineering datasets were also analyzed to highlight the applicability of the acquired point and interval estimators in an actual practical scenario.

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Section: Coating Weights Of Iron Sheetsmentioning

confidence: 99%

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Elshahhat

Mohammed

2023

Axioms

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“…This data set consists of 72 observations on coating weight (in gm/m 2 ) by chemical method on top-center side from the ALAF industry; see Table 2. This data set was first discussed by Rao and Mbwambo [35] and also analyzed by Fan and Gui [36] recently. To check whether the Dagum distribution is appropriate statistical distribution to fit the coating weight data set or not, the MLEs of the Dagum parameters α, β, and θ are calculated to carry out the Kolmogorov-Smirnov (K-S) distance and associated P-value.…”

Section: Coating Weights Of Iron Sheetsmentioning

confidence: 99%

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

et al. 2022

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In life testing and reliability studies, obtaining whole data always takes a long time and lots of monetary and human resources. In this case, the experimenters prefer to gather data using censoring schemes that make a balance between the length of the test, the desired sample size, and the cost. Lately, an adaptive progressive type-II hybrid censoring scheme is suggested to enhance the efficiency of the statistical inference. By utilizing this scheme, this paper seeks to investigate classical and Bayesian estimations of the Dagum distribution. The maximum likelihood and Bayesian estimation methods are considered to estimate the distribution parameters and some reliability indices. The Bayesian estimation is developed under the assumption of independent gamma priors and by employing symmetric and asymmetric loss functions. Due to the tough form of the joint posterior distribution, the Markov chain Monte Carlo technique is implemented to gather samples from the full conditional distributions and in turn obtain the Bayes estimates. The approximate confidence intervals and the highest posterior density credible intervals are also obtained. The effectiveness of the various suggested methods is compared through a simulated study. The optimal progressive censoring plans are also shown, and number of optimality criteria are explored. To demonstrate the applicability of the suggested point and interval estimators, two real data sets are also examined. The outcomes of the simulation study and data analysis demonstrated that the proposed scheme is adaptable and very helpful in ending the experiment when the experimenter’s primary concern is the number of failures.

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“…In the literature, statistical inferences have been made for different forms of the Rayleigh distribution, both in the case of complete and censored samples. Additionally, goodness-of-fit tests have been developed for the Rayleigh distribution (Sindhua et al [2], Dey and Dey [3], EL-Sagheer et al [4], Dey et al [5], Fan and Gui [6], Shen et al [7], Zamanzade and Mahdızadeh [8]).…”

Section: Introductionmentioning

confidence: 99%

Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine

Akdam

2023

Symmetry

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The aim of this study is to obtain the Bayes estimators and the maximum likelihood estimators (MLEs) for the unknown parameters of the Rayleigh–Weibull (RW) distribution based on progressive type-II censored samples. The approximate Bayes estimators are calculated using the idea of Lindley, Tierney–Kadane approximations, and also the Markov Chain Monte Carlo (MCMC) method under the squared-error loss function when the Bayes estimators are not handed in explicit forms. In this study, the approximate Bayes estimates are compared with the maximum likelihood estimates in the aspect of the estimated risks (ERs) using Monte Carlo simulation. The asymptotic confidence intervals for the unknown parameters are obtained using the MLEs of parameters. In addition, the coverage probabilities the parametric bootstrap estimates are computed. Real lifetime datasets related to bladder cancer, head and neck cancer, and leukemia are used to illustrate the empirical results belonging to the approximate Bayes estimates, the maximum likelihood estimates, and the parametric bootstrap intervals.

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Statistical Inference of Inverted Exponentiated Rayleigh Distribution under Joint Progressively Type-II Censoring

Cited by 14 publications

References 29 publications

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Statistical Analysis and Applications of Adaptive Progressively Type-II Hybrid Poisson–Exponential Censored Data

Analysis of Adaptive Progressive Type-II Hybrid Censored Dagum Data with Applications

Bayes Estimation for the Rayleigh–Weibull Distribution Based on Progressive Type-II Censored Samples for Cancer Data in Medicine

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